In this article, we investigate the integer sequence a d (n), where for a positive integer d, a d (n) is defined byIn particular, we will present a combinatorial model for a d (n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for a d (n). Moreover, we will show that p(n) − 2a d (n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.